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IEEE Transactions on Signal Processing
Article . 2005 . Peer-reviewed
License: IEEE Copyright
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Article . 2005
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IEEE Transactions on Signal Processing
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Piecewise fractional Brownian motion

descriptionPublicationkeyboard_double_arrow_right Article 01 Mar 2005Publisher:Institute of Electrical and Electronics Engineers (IEEE)Journal:IEEE Transactions on Signal Processing, volume 53, pages 1,211-1,215 (issn: 1053-587X, Copyright policy )
Authors: Perrin, Emmanuel; Harba, Rachid; Iribarren, Ileana; Jennane, Rachid;

doi: 10.1109/tsp.2004.842209

Piecewise fractional Brownian motion

Abstract

Starting from fractional Brownian motion (fBm) of unique parameter H, a piecewise fractional Brownian motion (pfBm) of parameters Hi, Ho and gamma is defined. This new process has two spectral regimes: It behaves like an fBm of parameter Ho for low frequencies and like an fBm of parameter Hi for high frequencies .When Ho = Hi, or for limit cases, pfBm becomes classical fBm. It is shown that pfBm is a continuous, Gaussian, and nonstationary process having continuous, Gaussian, and stationary increments, namely, piecewise fractional Gaussian noises. The asymptotic self-similarity of pfBm is shown according to the considered regime:At large scale, the process is self-similar with parameter and with parameter at low scale.

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Keywords

[SDV.IB] Life Sciences [q-bio]/Bioengineering, [SPI.ACOU] Engineering Sciences [physics]/Acoustics [physics.class-ph], [PHYS.PHYS.PHYS-MED-PH] Physics [physics]/Physics [physics]/Medical Physics [physics.med-ph], [SDV.MHEP] Life Sciences [q-bio]/Human health and pathology, self-similarity, [SPI.OPTI] Engineering Sciences [physics]/Optics / Photonic, [INFO.INFO-TS] Computer Science [cs]/Signal and Image Processing, [SPI.ELEC] Engineering Sciences [physics]/Electromagnetism, fractional Brownian motion, [INFO.INFO-IM] Computer Science [cs]/Medical Imaging, [SDV.IB.IMA] Life Sciences [q-bio]/Bioengineering/Imaging, [INFO.INFO-TI] Computer Science [cs]/Image Processing [eess.IV], Fractal, [PHYS.MECA.ACOU] Physics [physics]/Mechanics [physics]/Acoustics [physics.class-ph], [SPI.SIGNAL] Engineering Sciences [physics]/Signal and Image processing

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
15
Average
Top 10%
Average
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